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Beyond the Butterfly - A Graph-Theoretic Characterization of the Feasibility of Network Coding with Two Simple Unicast Sessions

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2 Author(s)
Chih-Chun Wang ; Purdue Univ., West Lafayette ; Shroff, N.B.

The problem of network coding with two simple unicast sessions is considered for general directed acyclic graphs. An explicit graph-theoretic characterization is provided for the feasibility of whether two symbols at different sources can be simultaneously transmitted to the designated sinks via network coding. The existence of a routing scheme is equivalent to finding edge-disjoint paths. Similarly, in this paper it is proven that the existence of a network coding scheme is equivalent to finding paths with controlled edge overlaps, and the characterization includes the well-studied butterfly graph as a special case. Various generalizations and implications are discussed based on the constructive nature of the flow-based conditions. For example, it is shown that a linear network coding scheme using only six paths is as effective as any non-linear network coding scheme.

Published in:

Information Theory, 2007. ISIT 2007. IEEE International Symposium on

Date of Conference:

24-29 June 2007